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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="common_with.html" title="cpp/concepts/common with"><span class="t-lines"><span>common_with</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5">                                 </td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="destructible.html" title="cpp/concepts/destructible"><span class="t-lines"><span>destructible</span></span></a></div></div></td></tr>
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<tr class="t-nv-h2"><td colspan="5"> 比较概念</td></tr>
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</td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="equality_comparable.html" title="cpp/concepts/equality comparable"><span class="t-lines"><span>equality_comparable</span><span>equality_comparable_with</span></span></a></div></div></td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><strong class="selflink"><span class="t-lines"><span>totally_ordered</span><span>totally_ordered_with</span></span></strong></div></div></td></tr>
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<tr class="t-nv-h2"><td colspan="5"> 对象概念</td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="movable.html" title="cpp/concepts/movable"><span class="t-lines"><span>movable</span></span></a></div></div></td></tr>
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<tr class="t-nv-h2"><td colspan="5"> 可调用概念</td></tr>
<tr class="t-nv-col-table"><td><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="invocable.html" title="cpp/concepts/invocable"><span class="t-lines"><span>invocable</span><span>regular_invocable</span></span></a></div></div></td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="predicate.html" title="cpp/concepts/predicate"><span class="t-lines"><span>predicate</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="relation.html" title="cpp/concepts/relation"><span class="t-lines"><span>relation</span></span></a></div></div></td></tr>
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<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="equivalence_relation.html" title="cpp/concepts/equivalence relation"><span class="t-lines"><span>equivalence_relation</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="strict_weak_order.html" title="cpp/concepts/strict weak order"><span class="t-lines"><span>strict_weak_order</span></span></a></div></div></td></tr>
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<table class="t-dcl-begin"><tbody>
<tr class="t-dsc-header">
<td> <div>定义于头文件 <code><a href="../header/concepts.html" title="cpp/header/concepts">&lt;concepts&gt;</a></code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-cxx20">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span> <span class="sy1">&lt;</span><span class="kw1">class</span> T<span class="sy1">&gt;</span><br>
<p>concept totally_ordered <span class="sy1">=</span><br>
  std<span class="sy4">::</span><span class="me2">equality_comparable</span><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span> <span class="sy3">&amp;&amp;</span><br>
  requires<span class="br0">(</span><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span><span class="sy3">&amp;</span> a,<br>
           <span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span><span class="sy3">&amp;</span> b<span class="br0">)</span> <span class="br0">{</span><br>
    <span class="br0">{</span> a <span class="sy1">&lt;</span>  b <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> a <span class="sy1">&gt;</span>  b <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> a <span class="sy1">&lt;=</span> b <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> a <span class="sy1">&gt;=</span> b <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
</p>
  <span class="br0">}</span><span class="sy4">;</span></span></div></td>
<td> (1) </td>
<td> <span class="t-mark-rev t-since-cxx20">(C++20 起)</span> </td>
</tr>
<tr class="t-dcl t-since-cxx20">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span> <span class="sy1">&lt;</span><span class="kw1">class</span> T, <span class="kw1">class</span> U<span class="sy1">&gt;</span><br>
<p>concept totally_ordered_with <span class="sy1">=</span><br>
  std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span> <span class="sy3">&amp;&amp;</span><br>
  std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1">&lt;</span>U<span class="sy1">&gt;</span> <span class="sy3">&amp;&amp;</span><br>
  std<span class="sy4">::</span><span class="me2">equality_comparable_with</span><span class="sy1">&lt;</span>T, U<span class="sy1">&gt;</span> <span class="sy3">&amp;&amp;</span><br>
  std<span class="sy4">::</span><span class="me2">totally_ordered</span><span class="sy1">&lt;</span><br>
    std<span class="sy4">::</span><span class="me2">common_reference_t</span><span class="sy1">&lt;</span><br>
      <span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span><span class="sy3">&amp;</span>,<br>
      <span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>U<span class="sy1">&gt;</span><span class="sy3">&amp;</span><span class="sy1">&gt;&gt;</span> <span class="sy3">&amp;&amp;</span><br>
  requires<span class="br0">(</span><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span><span class="sy3">&amp;</span> t,<br>
           <span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>U<span class="sy1">&gt;</span><span class="sy3">&amp;</span> u<span class="br0">)</span> <span class="br0">{</span><br>
    <span class="br0">{</span> t <span class="sy1">&lt;</span>  u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> t <span class="sy1">&gt;</span>  u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> t <span class="sy1">&lt;=</span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> t <span class="sy1">&gt;=</span> u <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> u <span class="sy1">&lt;</span>  t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> u <span class="sy1">&gt;</span>  t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> u <span class="sy1">&lt;=</span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
    <span class="br0">{</span> u <span class="sy1">&gt;=</span> t <span class="br0">}</span> <span class="sy2">-</span><span class="sy1">&gt;</span> std<span class="sy4">::</span><span class="me2">boolean</span><span class="sy4">;</span><br>
</p>
  <span class="br0">}</span><span class="sy4">;</span></span></div></td>
<td> (2) </td>
<td> <span class="t-mark-rev t-since-cxx20">(C++20 起)</span> </td>
</tr>
<tr class="t-dcl-sep"><td></td><td></td><td></td></tr>
</tbody></table>
<div class="t-li1"><span class="t-li">1)</span> 概念 <code>totally_ordered&lt;T&gt;</code> 指定比较运算符 <code>==,!=,&lt;,&gt;,&lt;=,&gt;=</code> 在 <code>T</code> 上产生的结果与 <code>T</code> 上的<a href="https://en.wikipedia.org/wiki/Total_order#Strict_total_order" class="extiw" title="enwiki:Total order">严格全序</a>一致。</div>
<div class="t-li1"><span class="t-li">2)</span> 概念 <code>totally_ordered_with&lt;T, U&gt;</code> 指定比较运算符 <code>==,!=,&lt;,&gt;,&lt;=,&gt;=</code> 在（可能混合的） <code>T</code> 和 <code>U</code> 运算数上产生的结果等价于比较转换到其共用类型的运算数的结果。</div>
<h3><span class="mw-headline" id=".E8.AF.AD.E4.B9.89.E8.A6.81.E6.B1.82">语义要求</span></h3>
<div class="t-li1"><span class="t-li">1)</span> <code>totally_ordered&lt;T&gt;</code> 仅若符合下列条件才得到实现。给定 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span></span></span> 类型左值 <code>a</code> 、 <code>b</code> 和 <code>c</code> ：
<ul><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&lt;</span> b<span class="br0">)</span></span></span> 、 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&gt;</span> b<span class="br0">)</span></span></span> 和 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">==</span> b<span class="br0">)</span></span></span> 恰有一者为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ；
</li><li> 若 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&lt;</span> b<span class="br0">)</span></span></span> 与 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1">&lt;</span> c<span class="br0">)</span></span></span> 均为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ，则 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&lt;</span> c<span class="br0">)</span></span></span> 为 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw2">true</span></span></span> ；
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&gt;</span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1">&lt;</span> a<span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&gt;=</span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="sy3">!</span><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&lt;</span> b<span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>a <span class="sy1">&lt;=</span> b<span class="br0">)</span> <span class="sy1">==</span> <span class="sy3">!</span><span class="kw4">bool</span><span class="br0">(</span>b <span class="sy1">&lt;</span> a<span class="br0">)</span></span></span></li></ul></div>

<div class="t-li1"><span class="t-li">2)</span> 正式而言， <code>totally_ordered_with&lt;T, U&gt;</code> 仅若符合下列条件才得到实现。给定 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span></span></span> 类型左值 <code>t</code> 和 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>U<span class="sy1">&gt;</span></span></span> 类型左值 <code>u</code> ，并令 <code>C</code> 为 <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">common_reference_t</span><span class="sy1">&lt;</span><span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>T<span class="sy1">&gt;</span><span class="sy3">&amp;</span>, <span class="kw4">const</span> <a href="../types/remove_reference.html"><span class="kw607">std::<span class="me2">remove_reference_t</span></span></a><span class="sy1">&lt;</span>U<span class="sy1">&gt;</span><span class="sy3">&amp;</span><span class="sy1">&gt;</span></span></span> ：
<ul><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">&lt;</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">&lt;</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">&gt;</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">&gt;</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">&lt;=</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">&lt;=</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>t <span class="sy1">&gt;=</span> u<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>t<span class="br0">)</span> <span class="sy1">&gt;=</span> C<span class="br0">(</span>u<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">&lt;</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">&lt;</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">&gt;</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">&gt;</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">&lt;=</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">&lt;=</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">bool</span><span class="br0">(</span>u <span class="sy1">&gt;=</span> t<span class="br0">)</span> <span class="sy1">==</span> <span class="kw4">bool</span><span class="br0">(</span>C<span class="br0">(</span>u<span class="br0">)</span> <span class="sy1">&gt;=</span> C<span class="br0">(</span>t<span class="br0">)</span><span class="br0">)</span></span></span></li></ul></div>

<h3><span class="mw-headline" id=".E7.9B.B8.E7.AD.89.E6.80.A7.E4.BF.9D.E6.8C.81">相等性保持</span></h3>
<p>若表达式对给定的相等输入产生相等输出，则它<i>保持相等性</i>。
</p>
<ul><li> 表达式的输入由其运算数组成。
</li><li> 表达式的输出由其结果和表达式所修改的所有运算数（若存在）组成。
</li></ul>
<p>进一步要求每个要求保持相等性的表达式都<i>稳定</i>：这种表达式带相同输入对象的二次求值必须拥有相等的输出，而无任何对这些输入对象的显式中间修改。
</p><p>除非另外提醒，每个用于 <i>requires 表达式</i>中的表达式都要求保持相等性且稳定，而表达式的求值必须只修改其非常运算数。必须不修改常运算数。
</p>
<h3><span class="mw-headline" id=".E9.9A.90.E5.BC.8F.E8.A1.A8.E8.BE.BE.E5.BC.8F.E5.8F.98.E7.A7.8D">隐式表达式变种</span></h3>
<p>使用不修改某 const 左值运算数的表达式的 <i>requires 表达式</i>亦隐式要求该表达式的额外变种对给定运算数接受非 const 左值或（可为 const 的）右值，除非以有区别的语义显式要求这种表达式变种。这些<i>隐式表达式变种</i>必须符合与声明的表达式的相同的语义。不指定实现以何种程度校验变种的语法。
</p>
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